Robust Wald Tests in SUR Systems with Adding Up Restrictions: An Algebraic Approach to Proofs of Invariance
In this paper, we examine the robust Wald test statistic for SUR systems with adding up restrictions where the same explanatory variables are present in all equations and where heteroskedasticity and/or autocorrelation of unknown forms may be present. For this case, the coefficients are usually estimated by least squares, equation by equation. For testing the typical hypotheses of interest, we show that the robust Wald statistic, i.e., the statistic based on the heteroskedasticity and autocorrelation consistent covariance matrix estimator, is invariant to the equation deleted. Our proof of invariance is algebraic and does not rely on parametric assumptions or on the knowledge of the covariance matrix of disturbances. Furthermore, the adding-up restrictions we consider are of a general form: the weighted sum of the dependent variables adds up to one of the explanatory variables, not necessarily a constant. We illustrate our results using the Capital Asset Pricing Model.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Barten, A. P., 1969. "Maximum likelihood estimation of a complete system of demand equations," European Economic Review, Elsevier, vol. 1(1), pages 7-73.
- Mandy, David M. & Martins-Filho, Carlos, 1993. "Seemingly unrelated regressions under additive heteroscedasticity : Theory and share equation applications," Journal of Econometrics, Elsevier, vol. 58(3), pages 315-346, August.
- Ravi Jagannathan & Ellen R. McGrattan, 1995. "The CAPM debate," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 2-17.
- White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
- Newey, Whitney & West, Kenneth, 2014.
"A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix,"
Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
- Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-708, May.
- Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
- Berndt, Ernst R & Savin, N Eugene, 1975. "Estimation and Hypothesis Testing in Singular Equation Systems with Autoregressive Disturbances," Econometrica, Econometric Society, vol. 43(5-6), pages 937-957, Sept.-Nov. Full references (including those not matched with items on IDEAS)